Liquid Density and Bubble Pressure Measurements for the Propylene

Mar 27, 2008 - Bubble pressures and liquid densities for the propylene (1) + 2-propanol (2) mixture have been determined at (300, 325, and 350) K and ...
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J. Chem. Eng. Data 2008, 53, 1167–1174

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Liquid Density and Bubble Pressure Measurements for the Propylene + 2-Propanol System Paolo Stringari,† Giancarlo Scalabrin,*,† Dominique Richon,‡ and Christophe Coquelet‡ Dipartimento di Fisica Tecnica, Università di Padova, via Venezia 1, I-35131 Padova, Italy, and Mines Paris Paris Tech, CEP/TEP, CNRS FRE 2861, 35, Rue Saint Honoré, 77305 Fontainebleau, France

Bubble pressures and liquid densities for the propylene (1) + 2-propanol (2) mixture have been determined at (300, 325, and 350) K and x1 close to 0.20, 0.52, and 0.65 using a vibrating tube densimeter. Liquid densities have been measured from bubble pressures up to 10 MPa and correlated with a multilayer feedforward neural network. The composition dependence of the excess molar volume has been evaluated in the temperature and pressure range of the experimental data. Bubble pressures have been compared with a multilayer feedforward neural network function regressed on the available literature data showing a good consistency between the two. The multilayer feedforward neural network correlations for liquid density and bubble pressure have been used to generate the saturated liquid density surface in the whole temperature range and for compositions including the pure components. Excess molar volumes and bubble pressure predictions obtained by the neural network models have been compared with those from a Peng–Robinson equation of state with Wong-Sandler mixing rules to show the consistent behavior in the regions where data are lacking.

1. Introduction The process industries, such as in particular the chemical ones, use a relevant fraction of their energy consumption for the separation processes of fluid mixtures. Apart from the conventional industrial separation processes, there is a rising need toward studying alternative methods compatible with the requirements of sustainable development, environmental impact, and energy saving. The limited knowledge of the thermodynamics of systems particularly complex, such as for instance the polar and associating mixtures, hinders the development of analysis and optimization studies addressed to both the overall effectiveness and the energetic consumption. In recent times, the separation processes of oxychemicals from aqueous solutions has received increasing consideration. The authors have previously considered an exemplifying system suitable for the development of an analyzing method for the present purpose which is 2-propanol + water + propylene.1 In general, the kind of data simultaneously needed are basically coexistence, density, and calorimetric data. In this context, a well-known lack of experimental data hinders pursuing of the scope so that the data of interest have to be expressly measured. In the present work, one of the binary mixtures composing the cited ternary system is studied, i.e., the propylene + 2-propanol one. The literature presents a number of experimental works about this mixture which in particular are: vapor–liquid equilibria at constant temperature in a range from (333.1 to 373.1) K in Zabaloy et al.;2 vapor pressure for diluted 2-propanol mixtures from (293.15 to 333.15) K in Guzechak et al.;3 bubble pressures * To whom correspondence should be addressed. Tel.: +39 049 827 6875. Fax: +39 049 927 6896. E-mail: [email protected]. † Università di Padova. ‡ Mines Paris Paris Tech.

at 298.15 K and excess enthalpies at 333.1 K and 3.1 MPa in Horstmann et al.4 For the density and bubble pressure measurements a “synthetic open circuit method” taking advantage of a vibrating tube densimeter (VTD) was used, allowing to quickly get efficient density data; in fact, this is one of the most popular measuring methods in the literature. A previous study concerning the determination of single phase densities and bubble pressures was done using the same technique for the carbon dioxide + 2-propanol system.5 The obtained liquid density and bubble pressure values have been correlated using two multilayer feedforward neural network (MLFN) functions.

2. Experimental 2.1. Chemicals. The 2-propanol (molar mass ) 60.096 kg · kmol-1, CAS Number 67-63-0) is from Sigma-Aldrich with a GC certified purity higher than 99.8 %. The propylene (molar mass ) 42.08 kg · kmol-1, CAS Number 115-07-1) is from Air–Liquide with a certified purity higher than 99.99 vol %. 2.2. Apparatus. A detailed description of the apparatus is given in ref 6, and its schematic layout is presented in Figure 1. The apparatus employs a vibrating tube made of stainless steel (Anton Paar, model DMA 512). The period of vibration τ is recorded by means of a data acquisition unit (Hewlett-Packard, model 53131A). The temperature of the vibrating tube is controlled by a regulated liquid bath (Lauda, model RE206) with stability within ( 0.01 K. The temperature of the remaining parts of the circuit is regulated by a liquid bath (Bioblock, model Variosat P1C50P as the cooling source, electric resistor managed by a PID regulator West model 6100 as the heating source). Temperatures are measured with two Pt 100 probes connected to a data acquisition unit (Hewlett-Packard, model 34970A). The probes have been calibrated in the (288 to 433) K range against a 25 Ω reference thermometer (Tinsley Precision

10.1021/je800017j CCC: $40.75  2008 American Chemical Society Published on Web 03/27/2008

1168 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008

Figure 1. Flow diagram of the equipment: 1, loading cell; 1a-1e, shut-off valves; 2a and 2b, regulating and shut-off inlet valves; 2c and 2d, regulating and shut-off outlet valves; 3, densimeter; 4, heat exchanger; 4a, bursting disk; 5a, 5b, and 6a, 6b, double valves; 7, inlet and outlet for the VTD temperature regulation; 8a and 8b, mixers; 9a and 9b, Pt 100 probes; 10, pressure transducers maintained at constant temperature; 11, data acquisition unit; 12, data acquisition unit; 13, data acquisition supervising; 14, temperature regulator of the pressure transducers; 15, temperature regulator of the thermostatted tube (20); 16, temperature regulator of the liquid bath (18); 17, temperature regulator of the main liquid bath; 18, liquid bath; 19, nitrogen bomb; 20, thermostatted tube.

Instrument) certified by Laboratoire National d’Essais (Paris, France). Pressure is measured using two pressure transducers (Druck, model PTX611) of two complementary ranges: (0 to 0.5) MPa and (0.5 to 8.0) MPa. These sensors were calibrated against a dead weight pressure balance (Desgranges & Huot, model 5202S) in the (0.3 to 10.6) MPa range. The vacuum was achieved by means of a vacuum pump (AEG, model LN38066008). Real time (τ, T, P) data are recorded every 3 s by a computer linked to both the HP units. Synthetic mixtures have been prepared gravimetrically under a vacuum according to the procedures presented in ref 7. An analytical balance (Sartorius AG, Göttingen, model CC3000) was used to get accurate mass values. Viton 70 Shore O-rings have been used as seals for the piston in the loading cell. 2.3. Experimental Procedure. The description of the experimental procedure refers to the schematic layout of the equipment presented in Figure 1. The synthetic mixture is gravimetrically prepared in the loading cell (1) under vacuum, according to the procedure discussed in ref 7. The loading cell is connected to the circuit by means of the valve 1c and to a high-pressure nitrogen bomb by the valves 1a and 1b. Before starting the measurement, the VTD liquid bath (18) is programmed at the measurement temperature, while the main bath is programmed at a temperature slightly higher, (0.5–1) K, to obtain the first vaporization inside the VTD instead of in the other parts of the circuit (for details, see ref 6). The whole circuit was evacuated connecting the vacuum pump to the valve 5a, while valves from 2a to 2d and 5b are open and valves 1c, 6a, and 6b are closed. The period of vibration at the lowest accessible pressure,

obtained with the vacuum pump, and at the measurement temperature is measured. To carry out density measurements in the liquid phase, the pressure in the loading cell is increased to values higher than the bubble pressure of the mixture to ensure the homogenization inside the cell. After the measurement of the vibration period at vacuum conditions, the vacuum pump is disconnected closing the valve 5a, and the fluid is loaded from the loading cell to the apparatus through the valve 1c. The movement of the piston inside the cell ensures the homogeneity of the mixture in the apparatus maintaining the mixture pressure constant during the loading of the circuit. If the loading pressure is higher than 0.5 MPa, the valve 1e has to be closed during this procedure to avoid damage of the lowpressure transducer. The circuit is partially purged, opening the valve 6a or 6b, and a new mixture is introduced in the circuit from the loading cell. It is assumed that the liquid inside the VTD is representative of the fluid inside the loading cell when the measured period of vibration remains constant and is not dependent on further purging. The pressure in the circuit is increased, opening the valve 1a up to the highest measurement pressure (about 10 MPa in this work). A suitable opening of the valve 2d is then selected to ensure that the pressure inside the circuit decreases continuously with a controlled rate not higher than 0.005 MPa · s-1. Under these conditions, the fluid inside the apparatus is assumed in mechanical equilibrium. The liquid phase is studied from the chosen upper pressure down to the bubble point, which is determined through the drastic change in the P ÷ τ behavior going from the single phase to the coexistence region as described in ref 6. During this process,

Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 1169 Table 1. Experimental Liquid Density Data for the Propylene (1) + 2-Propanol (2) Mixture x1 ) 0.2011 T ) 300.14 K P/PMa 0.5294 1.0513 1.4836 1.9544 2.3840 2.7986 3.2731 3.7402 4.1863 4.7286 5.2356 5.7673 6.2747 6.8325 7.2915 7.8118 8.2966 8.8103 9.3377 9.8864

F/kg · m

T ) 325.09 K -3

731.63 732.17 732.72 733.24 733.72 734.18 734.68 735.18 735.68 736.23 736.78 737.30 737.83 738.41 738.89 739.42 739.90 740.41 740.91 741.45

P/PMa 0.8109 1.2189 1.6087 2.0018 2.3837 2.8276 3.1592 3.7079 4.1236 4.5285 4.9253 5.3707 5.8835 6.3362 6.7884 7.3466 7.8793 8.3925 8.9852 9.5877

T ) 350.18 K -3

F/kg · m

703.07 703.59 704.14 704.70 705.30 705.86 706.38 707.07 707.68 708.19 708.73 709.32 709.98 710.58 711.17 711.90 712.57 713.18 713.89 714.65

P/PMa

F/kg · m-3

1.6395 2.0700 2.4462 2.9243 3.2714 3.6753 4.0584 4.4468 4.7913 5.1719 5.5574 6.0020 6.4302 7.0712 7.5705 7.9441 8.3868 8.8268 9.2790 9.7796

677.13 677.93 678.64 679.50 680.17 680.86 681.60 682.32 682.93 683.60 684.26 684.96 685.69 686.73 687.62 688.25 688.92 689.60 690.38 691.08

x1 ) 0.5201 T ) 300.11 K

T ) 325.05 K

T ) 350.12 K

P/PMa

F/kg · m-3

P/PMa

F/kg · m-3

P/PMa

F/kg · m-3

0.9667 1.3733 1.8356 2.3409 2.8124 3.3301 3.8175 4.3861 4.8737 5.3752 5.8888 6.4420 6.9428 7.4982 8.1047 8.6718 9.2267 9.7870

644.49 645.21 645.98 646.83 647.62 648.49 649.27 650.18 650.95 651.72 652.52 653.35 654.09 654.90 655.77 656.58 657.35 658.16

1.6131 1.9777 2.3590 2.7172 3.1678 3.5061 3.8888 4.3216 4.6767 5.0614 5.4718 5.8801 6.2936 6.7043 7.1717 7.5974 8.0375 8.5565 9.0781 9.6313

613.41 614.26 615.15 615.98 616.93 617.74 618.59 619.52 620.29 621.12 621.94 622.78 623.65 624.42 625.34 626.18 627.02 628.02 628.97 629.98

2.3323 2.7314 2.9924 3.2180 3.5061 3.7656 4.2255 4.5506 4.8244 5.1037 5.3993 5.7155 5.9995 6.3039 6.6328 6.9755 7.2800 7.6413 7.9635 8.3120 8.7624 9.2110 9.6229

576.59 577.92 578.85 579.68 580.58 581.46 582.95 583.87 584.73 585.64 586.54 587.44 588.29 589.18 590.10 591.05 591.94 592.87 593.76 594.68 595.82 596.88 597.92

x1 ) 0.6478 T ) 300.12 K P/PMa F/kg · m-3 1.0685 608.06 1.4865 608.93 1.7406 609.48 2.1238 610.19 2.6200 611.17 2.9868 611.92 3.4953 612.85 3.8290 613.59 4.1935 614.26 4.5428 614.93 4.9054 615.61 5.2637 616.27 5.6341 616.94 6.0113 617.61 6.3953 618.28 6.7886 618.96 7.1654 619.61 7.5581 620.28 7.9601 620.96 8.3772 621.66 8.7855 622.34 9.2342 623.05 9.6821 623.79

T ) 325.13 K P/PMa F/kg · m-3 1.7475 573.29 2.1518 574.52 2.6075 575.84 3.0221 577.00 3.4227 578.16 3.8263 579.23 4.2890 580.41 4.6825 581.48 5.0946 582.53 5.5248 583.59 5.9722 584.68 6.4310 585.75 6.9233 586.94 7.4335 588.03 7.9350 589.22 8.4599 590.39 9.0240 591.62 9.5585 592.78

T ) 350.18 K P/PMa F/kg · m-3 2.6890 531.01 3.1263 533.02 3.6862 535.68 3.9143 536.74 4.2032 537.97 4.4846 539.15 4.7385 540.50 5.0234 541.63 5.3212 542.86 5.6140 543.95 5.9389 545.10 6.2684 546.35 6.6221 547.76 6.9786 548.98 7.3620 550.27 7.7365 551.56 8.1262 552.91 8.5255 554.11 8.9798 555.58 9.4880 557.04 9.9898 558.59

Figure 2. Liquid density measurements for the propylene (1) + 2-propanol (2) mixture.

the pressure, the temperature inside the VTD, and the period of vibration are recorded every 3 s. The period of vibration is converted into density using the Forced Path Mechanical Calibration (FPMC) method.8 The first reference for the calibration is the period of vibration measured at vacuum conditions, while the second reference is with the refrigerant R134a, for which measurements have been carried out at the same temperature and in the same pressure range of the target mixture (see ref 8). 2.4. Experimental Uncertainties. The experimental uncertainties have been calculated taking into account the expanded uncertainties and coverage factor as described in ref 9. The global uncertainty on density data in the liquid phase is estimated to be within 0.05 %. The uncertainty on vibrating period values is ( 10-8 s. Global temperature uncertainties are estimated to be about ( 0.02 K with a confidence level of approximately 68 %. Global uncertainties on pressure measurement are ( 0.0001 MPa (for (0 < P e 0.6) MPa) and ( 0.0006 MPa (for (0.6 < P e 10.6) MPa) with a confidence level of approximately 68 %. Uncertainties in mixture composition are within 2 · 10-4 in molar fraction.

3. Experimental Results 3.1. Liquid Density Results. The liquid density measurements for the propylene (1) + 2-propanol (2) mixture have been carried out at (300, 325, and 350) K from 10 MPa down to bubble pressures for the x1 ) (0.20, 0.52, and 0.65) molar fractions. The measured (P, F, T) values are reported in Table 1. In Figure 2, the measured data are shown together with liquid density values of the pure propylene10 and 2-propanol11 at the same temperatures of the mixture measurements and for pressures from the pure fluid bubble points up to 10 MPa. Temperature dependence at constant composition of the propylene (1) + 2-propanol (2) mixture is shown in Figure 3a, while composition dependence at constant temperature is shown in Figure 3b. 3.2. Equilibrium Results. The VTD allows us to obtain density measurements, and furthermore, through a data reduction of such values, bubble pressures can also be evaluated as discussed in ref 6. In this way, bubble pressures for the propylene (1) + 2-propanol (2) mixture have been obtained at (300, 325, and 350) K for x1 ) (0.20, 0.52, and 0.65) molar fractions. The values are reported in Table 2, while the Figure 4 shows the obtained values in comparison to the available literature data in the same temperature range.2–4

1170 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008

Figure 3. Propylene (1) + 2-propanol (2) mixture: (a) temperature dependence of the liquid density at constant composition (x1 ) 0.20); (b) composition dependence of the liquid density at constant temperature (T ) 300 K). Table 2. Comparison of Pressures and Densities at Bubble Point Conditions between Those Determined by the VTD (P and G) and Those by the Intersection of the Compressed Liquid Density MLFN Model and the Bubble Pressure MLFN Model (P′ and G′) T

x1

P

P′

∆P

K

(molar)

MPa

MPa

%

300.14 300.11 300.12 325.09 325.05 325.13 350.18 350.12 350.18

0.2011 0.5201 0.6478 0.2011 0.5201 0.6478 0.2011 0.5201 0.6478

0.5224 0.9192 1.0297 0.7850 1.5583 1.7095 1.2620 2.1521 2.6200

0.4956 -5.125 0.9199 0.076 1.0021 -2.677 0.8604 9.606 1.5658 0.481 1.7394 1.748 1.2840 1.743 2.3275 8.149 2.6342 0.542

F

F′

kg · m-3 kg · m-3 731.63 644.42 607.97 703.01 613.29 573.24 676.38 575.99 530.66

731.23 644.63 607.84 703.25 613.39 573.50 676.63 576.57 530.79

∆F % -0.055 0.032 -0.022 0.034 0.017 0.045 0.037 0.102 0.025

4. Modeling Methods Multilayer feedforward neural network (MLFN) functional forms have been used to correlate liquid density and bubble pressure experimental values. The general architecture of a Figure 5. General topology of a three-layer feedforward neural network.

MLFN is illustrated in Figure 5: it is composed of a certain number of units, called neurons, organized in three layers called the input, hidden, and output layers, respectively. The neurons j of of the input layer are indicated as elements of an array U dimension I. Their number coincides with the number of independent variables of the equation plus one. The last neuron, labeled Bias 1, has a constant value

UI ) Bias 1

(1)

The number of neurons of the output layer equals the output quantities, which are elements of an array Sj of dimension K. The hidden layer performs the transformation of the signals from the input layer to the output layer, and it can contain an j arbitrary number of neurons. These are elements of an array H of dimension J + 1. Also in the hidden layer, there is a bias neuron with a constant value, Bias 2

HJ+1 ) Bias 2 Figure 4. Bubble pressure data for the propylene (1) + 2-propanol (2) mixture.

(2)

The physical input variables Vi (temperature, pressure, and mole fraction for the liquid density correlation and temperature

Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 1171 Table 3. Parameters of the Feedforward Neural Network Used for the Correlation of the Liquid Density Data for the Mixture Propylene (1) + 2-Propanol (2) β ) 0.5

Vmin,1 ) Tmin ) 250

Vmax,1 ) Tmax ) 400

I)4

Vmin,2 ) Pmin ) 0

Vmax,2 ) Pmax ) 12

J ) 12

Vmin,3 ) xmin ) 0

Vmax,3 ) xmax ) 1

K)1 i 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2

Wmin,1 ) Fmin ) 350

j

wij

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

9.010170 · 10 -7.888430 4.093740 3.175850 · 101 5.408060 1.160290 · 101 -1.719460 2.384800 · 101 -1.635840 · 102 7.722330 · 102 9.913330 2.627740 · 10-1 -3.232040 · 101 -6.101320 · 10-2 9.660710 · 10-4 -4.646080 · 101 -5.914600 · 10-1 -7.413220 1.424330 2.367740 · 101 9.005100 · 101 -4.175130 · 102 -7.045390 · 10-1 1.699010

i 1

3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4

Wmax,1 ) Fmax ) 800

j

wij

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

1.119710 · 10 -9.451570 4.741180 · 101 3.745950 · 101 4.226020 6.257430 · 101 -6.859890 · 101 3.126750 · 101 -5.275310 · 101 2.476070 · 102 8.709160 -9.278200 · 101 -1.615050 · 102 2.656600 · 101 1.236170 · 102 6.156810 · 101 -4.362300 · 10-1 -6.507460 · 101 -1.663850 3.043150 · 101 1.339450 · 102 -6.333350 · 102 -9.259080 · 10-1 -2.553360 2

j

k

wjk

1 2 3 4 5 6 7 8 9 10 11 12 13

1 1 1 1 1 1 1 1 1 1 1 1 1

-4.617640 · 101 1.045780 · 102 2.705210 · 101 -3.218450 · 101 4.131650 · 101 1.148660 7.869950 · 101 7.177710 · 101 -1.563460 · 102 -7.446350 · 102 -8.324710 · 101 -7.044190 · 101 3.140790 · 101

Table 4. Accuracy of the Feedforward Neural Network Model in the Representation of the Liquid Density Data of the Propylene (1) + 2-Propanol (2) Mixture system

ref

NPTa

T range (K)

P range (MPa)

x1 range

AAD (%)

Bias (%)

MAD (%)

binary mixture 2-propanol propylene

this work Stringari et al.11 Angus et al. (DEoS)10

186 123 98 407

300.0 to 350.2 300.0 to 350.0 300.0 to 350.0 300.0 to 350.2

0.0 to 10.1 0.0 to 10.0 1.2 to 10.1 0.0 to 10.1

0.20 to 0.65 0.00 1.00 0.00 to 1.00

0.017 0.019 0.028 0.020

0.006 0.008 0.014 0.009

0.063 0.035 0.099 0.099

a

NPT: number of experimental points.

and composition for the bubble pressure correlation) undergo a linear transformation to normalize them in the arbitrarily chosen range [Amin, Amax] set as Amin ) 0.05 and Amax ) 0.95

Ui ) ui(Vi - Vi,min) + Amin

1eieI-1

for

(3)

where

ui )

Amax - Amin Vi,max - Vi,min

(4)

and Vi,min and Vi,max represent the selected extremes of the range of the variable Vi. An arctangent function normalized in the range [0,1] is assumed as the transfer function

1 g(z) ) arctan(β · z) + 0.5 π

(5)

The transfer function calculates the signal output of a neuron from its inputs for both the hidden and the output layer neurons; respectively, it is

(∑ ) (∑ ) I

Hj ) g

wijUi

for

1ejeJ

(6)

i)1

(7)

Figure 6. Percentage error of the feedforward neural network model in the representation of the liquid density data of the propylene (1) + 2-propanol (2) mixture: C3 ) propylene, IPA ) 2-propanol.

The symbols wij and wjk indicate the weighting factors that are the free parameters of the model, which must be determined

in the regression process. The output values Sk of the output layer neurons are denormalized to real output variables Wk,

J+1

Sk ) g

wijkUj

for

1ekeK

j)1

1172 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008

Figure 7. Excess molar volumes for the propylene (1) + 2-propanol (2) mixture: (a) pressure dependence at constant temperature; (b) temperature dependence at constant pressure.

which are in this case either density or bubble pressure, through the following linear transformation

Wk )

Sk - Amin + Wk,min sk

for

1ekeK

(8)

where

sk )

Amax - Amin Wk,max - Wk,min

(9)

Wk,min and Wk,max are the chosen limits of the range of the dependent variable Wk.

5. Discussion The measured values of liquid density and bubble pressure for the propylene (1) + 2-propanol mixture have been represented with MLFN functions presented in the previous section, and a statistical analysis of the data representation is reported in the following. In such a context, the error deviation ∆Mi of the ith point of a property M, the percentage average absolute deviation AAD %, the Bias %, and the percentage maximum absolute deviation MAD % with respect to a database of NPT values are evaluated as

∆Mi )

(

Mcalcd - Mexptl Mexptl

)

(10) i

NPT

AAD % ) 100 ·

∑

1 |∆Mi| NPT i)1

(11)

NPT

∑

1 ∆Mi Bias % ) 100 · NPT i)1

(12)

MAD % ) 100 · max |∆Mi|

(13)

i)1,NPT

M represents here the liquid density F or the bubble pressure pbub.

The measured liquid density values, together with the liquid density values of pure propylene10 and of pure 2-propanol,11 at the same temperatures of the mixture measurements and for pressures ranging from the pure fluid bubble points up to 10 MPa, were correlated with a MLFN. The parameters used for the correlation of the liquid density data are presented in Table 3. Residual errors are presented in Table 4 and shown graphically in Figure 6. The simultaneous representation of mixture and pure fluid data shows a good coherence among the measured liquid density values for the mixture and independent density values for the pure fluids. Using the obtained MLFN function, excess molar volumes have been calculated, and their composition dependence has been shown, varying pressure at constant temperature, in Figure 7a, and varying temperature at constant pressure, in Figure 7b. In the same figures, also the excess molar volumes calculated with the Peng–Robinson EoS including the Wong-Sandler mixing rules as obtained for this system in ref 1 have been shown for comparison. A very good agreement between experimental excess volume values and values predicted by the MLFN can be noted in Figure 7. This result comes from the very low residual error (AAD % ) 0.0201) in the representation of the pure fluids and mixture density values with the MLFN. On the other hand the Peng–Robinson EoS1 represents the excess molar volumes only in a qualitative way, confirming that such an EoS is not precise enough in the representation of compressed liquid densities, especially for systems involving associating fluids. The coefficients of a second MLFN have been regressed on the literature bubble pressure values2,4 and on the saturation pressure of the pure propylene10 and pure 2-propanol.12 The parameters used for the correlation of the bubble pressure data are presented in Table 5. The percentage errors of the obtained MLFN with respect to the measured bubble pressures are presented in Table 6 together with the errors with respect to the literature data available in the same range of temperatures. The AAD % with respect to the measured values is greater

Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008 1173 Table 5. Parameters of the Feedforward Neural Network Used for the Correlation of the Bubble Pressure Data for the Mixture Propylene (1) + 2-Propanol (2) β ) 0.5

Vmin,1 ) Tmin ) 250

Vmax,1 ) Tmax ) 400

I)3

Vmin,2 ) xmin ) 0

Vmax,3 ) xmax ) 1

J ) 10

Wmin,2 ) Pminbub ) 0

Wmax,1 ) Pmaxbub ) 12

K)1 i

j

wij

i

j

wij

j

k

wjk

1 1 1 1 1 1 1 1 1 1 2 2 2 2 2

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5

-2.984260 -2.368580 -5.797060 · 10-2 -7.176010 8.495830 5.252270 -6.099100 -1.445960 -3.605730 · 101 9.521860 -1.685540 · 10-1 -5.177630 -3.103680 · 101 -4.547720 1.348860 · 101

2 2 2 2 2 3 3 3 3 3 3 3 3 3 3

6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

-8.020910 -1.477240 · 101 1.219770 6.848890 · 101 2.736060 2.109340 5.568850 9.371590 · 10-1 4.846480 -4.758900 -4.523590 4.351610 5.681530 · 10-2 -5.409480 · 101 -4.652040

1 2 3 4 5 6 7 8 9 10 11

1 1 1 1 1 1 1 1 1 1 1

-4.286830 · 101 1.003870 · 101 -1.594220 · 101 1.780930 · 101 -3.840020 · 101 6.209550 -3.350460 · 101 5.234110 · 101 5.640040 · 10-1 2.152770 · 101 5.090110

Table 6. Accuracy of the Feedforward Neural Network Model in the Representation of the Bubble Pressure Data of the Propylene (1) + 2-Propanol (2) Mixture ref

NPT

T range (K)

P range (MPa)

x1 range

AAD (%)

Bias (%)

MAD (%)

this work Horstmann et al.4 Zabaloy et al.2 Guzechak et al.3

9 17 17 12 55

300.1 to 350.2 298.1 333.1 to 353.1 293.2 to 333.2 300.1 to 353.1

0.5 to 2.6 0.2 to 1.1 0.6 to 3.4 0.2 to 0.7 0.2 to 3.4

0.20 to 0.65 0.08 to 1.00 0.08 to 0.94 0.02 to 0.15 0.02 to 1.00

3.350 0.506 0.794 50.999 12.077

1.616 0.191 –0.037 –50.999 –10.815

9.606 2.594 2.223 59.794 59.794

than the AAD % with respect to the literature data on which the weighting factors of the MLFN have been regressed. The AAD of the measured bubble pressures is about 3.35 %, while a value significantly lower is found for the literature data of refs 2 and 4. At the same time, it can be noted that literature data from ref 3 are not at all consistent with all the other bubble pressure data. A comparison between the MLFN predictions and the measured bubble pressures is shown in Figure 4. In the same figure, the bubble pressures predicted by the MLFN are compared with the Peng–Robinson EoS using Wong-Sandler mixing rules, whose parameters were presented in ref 1. From the intersection of the MLFN function regressed on single phase liquid densities and the MLFN function regressed

on bubble pressures, it is possible to obtain an accurate representation of the saturated liquid density surface of the mixture as a function of temperature and composition. Figure 8 shows several isothermal sections of such a surface pointing out the regular trends in the saturated liquid density representation by the developed model. Using the same approach, the saturated liquid densities at the present experimental temperature and composition values have been calculated, and the results are reported in Table 2 as F′. In the same table, the bubble pressures calculated by the MLFN model P′ are also reported for comparison. The percentage relative deviation among the two evaluation methods of the saturated liquid density is quite close to the experimental uncertainty of the density measurements. The percentage deviations among the bubble pressures determined from the experimental data through the graphical procedure and the corresponding ones generated by the MLFN model are also reported in the table. Reference is also made to former Table 6 and its relative comments.

6. Conclusions Liquid densities for the propylene (1) + 2-propanol (2) mixture have been measured at (300, 325, and 350) K from 10 MPa down to bubble pressures and x1 ) (0.20, 0.52, and 0.65) molar fractions. The measured liquid density values have been correlated with a MLFN including liquid density values of the pure components, showing a good consistency of the mixture measurements with the pure fluid data. Excess molar volumes have been calculated, and their trend is consistent with the Peng–Robinson EoS using Wong-Sandler mixing rules. Figure 8. Saturated liquid density prediction for the propylene (1) + 2-propanol (2) mixture obtained as intersection of the feedforward neural network correlations for the liquid densities and for the bubble pressures.

Bubble pressures for the propylene (1) + 2-propanol (2) mixture have been obtained at (300, 325, and 350) K and x1 ) (0.20, 0.52, and 0.65) molar fractions. The measured values have been compared with a MLFN function with coefficients

1174 Journal of Chemical & Engineering Data, Vol. 53, No. 5, 2008

regressed on literature data in the same range of temperatures of the measurements carried out in this work. The saturated liquid density surface in the temperature and pressure range of the measurements presented in this work has been obtained as an intersection of the MLFN function regressed on single-phase liquid densities and the MLFN function regressed on bubble pressures.

Literature Cited (1) Grigiante, M.; Stringari, P.; Scalabrin, G.; Ihmels, C.; Fischer, K.; Gmehling, J. Vapor-liquid-liquid equilibria and excess molar enthalpies of binary and ternary mixtures of 2-propanol, water, and propylene. J. Chem. Thermodyn. 2007, doi: 10.1016/j.jct.2007.12.002. (2) Zabaloy, M.; Mabe, G.; Bottini, S. B.; Brignole, E. A. Isothermal vapor-liquid equilibrium data for the binaries propane-2-propanol and propylene-2-propanol. J. Chem. Eng. Data 1993, 38, 40–43. (3) Guzechak, O. Y.; Sarancha, V. N.; Romanyuk, I. M.; Yavorskaya, O. M.; Churik, G. P. Solubility of propylene in organic solvents. J. Appl. Chem. USSR 1984, 57, 1663–1665. (4) Horstmann, S.; Gardeler, H.; Bölts, R.; Rarey, J.; Gmehling, J. Isothermal Vapor-Liquid Equilibrium and Excess Enthalpy Data for the Binary Systems Diethyl Ether + Ethyl tert-Butyl Ether, 1-Pentene + Methyl Acetate, and Propene + 2-Propanol. J. Chem. Eng. Data 1999, 44, 383–387. (5) Khalil, W.; Coquelet, C.; Richon, D. High-Pressure Vapor-Liquid Equilibria, Liquid Densities, and Excess Molar Volumes for the Carbon

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Dioxide + 2-Propanol System from (308.10 to 348.00) K. J. Chem. Eng. Data 2007, 52, 2032–2040. Bouchot, C.; Richon, D. Direct Pressure-Volume-Temperature and Vapor-Liquid Equilibrium Measurements with a Single Equipment Using a Vibrating Tube Densimeter up to 393 K and 40 MPa: Description of the Original Apparatus and New Data. Ind. Eng. Chem. Res. 1998, 37, 3295–3304. Galicia-Luna, L. A.; Richon, D.; Renon, H. New Loading Technique for a Vibrating Tube Densimeter and Measurements of Liquid Densities up to 39.5 MPa for Binary and Ternary Mixtures of the Carbon Dioxide-Methanol-Propane System. J. Chem. Eng. Data 1994, 39, 424–431. Bouchot, C.; Richon, D. An enhanced method to calibrate vibrating tube densimeters. Fluid Phase Equilib. 2001, 191, 189–208. Taylor, B. N.; Kuyatt, C. E. NIST Technical Note 1297, National Institute of Standards and Technology: Gaithersburg, MD, 1994 (see also at: http://physics.nist.gov/cuu/Uncertainty/index.html). Angus, S.; Armstrong, B.; de Reuck, K. M., International Thermodynamic Tables of the Fluid State-7 Propylene, International Union of Pure and Applied Chemistry; Pergamon Press: Oxford, 1980. Stringari, P.; Scalabrin, G.; Richon, D. Density measurements of 2-propanol in the liquid region. 2008, submitted for publication. Poling, B. E. Vapor pressure prediction and correlation from the triple point to the critical point. Fluid Phase Equilib. 1996, 116, 102–109.

Received for review January 7, 2008. Accepted February 1, 2008. P. Stringari is grateful to Fondazione Ing. Aldo Gini (Padova, Italy) for financial support.

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